
Sparse signal detection. Suppose we are interested in intercepting a transmission that occupies few frequency bands out of potentially many, while the occupied bands are unknown to us [1]}. As an example, the set of features for testing the presence of transmission consists of the periodogram ordinate associated with each frequency band.

Classification. Classifying images or other high-dimensional signals usually involves thousands of features.
We think about the typical response of each feature under a specific base class as the global null hypothesis. Testing against this null amounts to determining whether the tested signal is associated with the base class or not. A situation of wide interest is when inter-class discrimination is due to few features out of potentially many [2]}.

Detecting changes from a reference dataset.
Testing whether two high-dimensional datasets are simply two different realizations of the same data generating mechanism is a classical problem in statistics, computer science, and information theory [3]}, [4]}, [5]}. This scenario is formulated as a two-sample testing problem; the null hypothesis states that both samples were obtained from the same high-dimensional parent distribution.

